Proof step e-fcc9671b64420c56

gamma_polynomial scale 1, shift 0 → concludes about gamma_polynomial of type_b_eulerian JSON

Theorem

Gamma criterion RealRooted IsGammaExpansion.isRealRooted_and_hasRootsNonpos_iff ?

Operation

Gamma polynomial of a palindromic parent

{
  "index_shift": 0,
  "operation": "gamma_polynomial",
  "scale": "1"
}

Premises

• type_b_eulerian (sequence)
  uses: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]

Claims

• { "claim": "real_rooted", "from_index": 0, "region": { "upper": { "closed": true, "value": "0" } } }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: gamma_polynomial, SHA-256 ae2df29437a82d2081d2b6d35118bdb4de13f7cf47c6c608bad8feea5482c339, 10,113 bytes (2,281 compressed); download JSON

Cited by

• n-7b489708d21ffcfe (real_rooted)
• n-7b489708d21ffcfe (one_signed_coefficients)
• n-7b489708d21ffcfe (hadamard_kernel)